We analyze the role of temperature in the rate-independent cohesion and decohesion behavior of an elastic film, mimicked by a one-dimensional mass-spring chain, grounded to an undeformable sub-strate via a one-dimensional sequence of breakable links. In the framework of equilibrium statistical mechanics, in both isometric (Helmholtz ensemble) and isotensional (Gibbs ensemble) conditions, we prove that the decohesion process can be described as a transition at a load threshold, sensibly depending on temperature. Under the classical assumption of having a single domain wall between attached and detached links (zipper model), we are able to obtain analytical expressions for the temperature dependent decohesion force, qualitatively reproducing important experimental effects in biological adhesion. Interestingly, although the two ensembles exhibit a similar critical behavior, they are not equivalent in the thermodynamic limit since they display dissimilar force-extension curves and, in particular, significantly different decohesion thresholds.